- commit of the "s_computation" component ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / fsb_aaa.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_aaa.ma
index 5a8d5d2408d9beee1b0d2191349b82e52982cf5d..05bb29c012c541bf46b1a1cc9862ebd37a558616 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fsb_aaa.ma
@@ -21,50 +21,50 @@ include "basic_2/computation/fsb_csx.ma".
 (* Main properties **********************************************************)
 
 (* Note: this is the "big tree" theorem ("RST" version) *)
-theorem aaa_fsb: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦥[h, g] ⦃G, L, T⦄.
+theorem aaa_fsb: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦥[h, o] ⦃G, L, T⦄.
 /3 width=2 by aaa_csx, csx_fsb/ qed.
 
 (* Note: this is the "big tree" theorem ("QRST" version) *)
-theorem aaa_fsba: ∀h,g,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦥⦥[h, g] ⦃G, L, T⦄.
+theorem aaa_fsba: ∀h,o,G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → ⦥⦥[h, o] ⦃G, L, T⦄.
 /3 width=2 by fsb_fsba, aaa_fsb/ qed.
 
 (* Advanced eliminators on atomica arity assignment for terms ***************)
 
-fact aaa_ind_fpb_aux: ∀h,g. ∀R:relation3 genv lenv term.
+fact aaa_ind_fpb_aux: ∀h,o. ∀R:relation3 genv lenv term.
                       (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                    (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                                    (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
                                     R G1 L1 T1
                       ) →
-                      ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
-#h #g #R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T
+                      ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
+#h #o #R #IH #G #L #T #H @(csx_ind_fpb … H) -G -L -T
 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
-#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf h g … G2 … L2 … T2 … HTA1) -A1
+#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf h o … G2 … L2 … T2 … HTA1) -A1
 /2 width=2 by fpb_fpbs/
 qed-.
 
-lemma aaa_ind_fpb: ∀h,g. ∀R:relation3 genv lenv term.
+lemma aaa_ind_fpb: ∀h,o. ∀R:relation3 genv lenv term.
                    (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
                                  R G1 L1 T1
                    ) →
                    ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
 /4 width=4 by aaa_ind_fpb_aux, aaa_csx/ qed-.
 
-fact aaa_ind_fpbg_aux: ∀h,g. ∀R:relation3 genv lenv term.
+fact aaa_ind_fpbg_aux: ∀h,o. ∀R:relation3 genv lenv term.
                        (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                     (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                                     (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≡[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
                                      R G1 L1 T1
                        ) →
-                       ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
-#h #g #R #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
+                       ∀G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, o] T → ∀A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.
+#h #o #R #IH #G #L #T #H @(csx_ind_fpbg … H) -G -L -T
 #G1 #L1 #T1 #H1 #IH1 #A1 #HTA1 @IH -IH //
-#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf h g … G2 … L2 … T2 … HTA1) -A1
+#G2 #L2 #T2 #H12 elim (fpbs_aaa_conf h o … G2 … L2 … T2 … HTA1) -A1
 /2 width=2 by fpbg_fwd_fpbs/
 qed-.
 
-lemma aaa_ind_fpbg: ∀h,g. ∀R:relation3 genv lenv term.
+lemma aaa_ind_fpbg: ∀h,o. ∀R:relation3 genv lenv term.
                     (∀G1,L1,T1,A. ⦃G1, L1⦄ ⊢ T1 ⁝ A →
-                                  (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
+                                  (∀G2,L2,T2. ⦃G1, L1, T1⦄ >≡[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
                                   R G1 L1 T1
                     ) →
                     ∀G,L,T,A. ⦃G, L⦄ ⊢ T ⁝ A → R G L T.